A Not Always Right customer is one that is 1. Trying to get something for nothing; 2. Abusing the employee for one reason or another (trying to get their own way, or for the fun of it); 3. Doesn't realize they're wrong.
(The Customer is) Not Always Right is a website dedicated to stories of the stupid, ignorant, egotistical, funny and just plain mad customers whom retail staff across the world (well, mostly in the Anglo-sphere — since it's an English-only site) encounter. It can be a good example of Tropes that appear in Real Life. That being said, it is best to take most of it with a grain of salt.
In 2011, two sister sites were launched: Not Always Romantic and Not Always Related. In 2012, they added Not Always Working to the collective, followed by Not Always Learning in 2013, Not Always Friendly in 2014, Not Always Hopeless in 2016 (demoted to a separate "Inspirational" category in 2019), Not Always Healthy in 2017, and Not Always Legal in 2018.
As of May 2017, all the sites were merged into one site.